The resistive tearing mode instability is a mechanism that in some cases will render unstable a magnetohydrodynamic equilibrium of a plasma that is ideally stable, i.e. stable if no dissipative oiesses are taken into account. There is much experimental evidence that this instability is the cause of the current disruptions observed in laboratory plasma devices (von Goeler et al. 1974). In the astrophysical context, the instability has been invoked in connection with the solar flare energy release mechanism (Coppi and Friedland 1971) and the problem of the disconnection of the protostar matter from the interstellar magnetic field during star formation (Mestel 1966). In the latter problem the tearing instability gives rise to a much smaller timescale for magnetic reconnection than does ordinary resistive diffusion.